Traveling nose of a glacier with linear basal drag ($s=\frac{\rho g}{\mu v}(h^3/9+h^2/(2\beta ))$)

A locally steady glacier nose moving at speed $v>0$ has $q=vh$ by mass conservation. At distance $s$ behind its edge, the linear basal drag law then gives $s=(\rho g/\mu v)(h^3/9+h^2/(2\beta ))$. The thin nose has $h\propto s^{1/2}$ from basal sliding; a thicker outer nose has $h\propto s^{1/3}$ from internal deformation. A thick bulk therefore still has a sliding-controlled inner tip. The divergent idealized edge slope limits the immediate validity of the shallow-ice approximation.